How do you factor #25 g^3 v^3 + 15 g^2 e^3 v^3 + 5 g b d + 3 e^3 b d#?

1 Answer
Alan P.
Jun 22, 2016

#25g^3v^3+15g^2e^3v^3+5gbd+3e^3bd=color(blue)((5g^2v^3+bd)(5g+3e^3))#

Explanation:

Note 1:
#color(white)("XXX")#The first two terms have a common factor of
#color(white)("XXXXXX")5g^2v^3#
#color(white)("XXX")25g^3v^3+15g^2e^3v^3=(color(red)(5g^2v^3))(5g+3e^3)#

Note 2:
#color(white)("XXX")#The last two terms have a common factor of
#color(white)("XXXXXX")bd#
#color(white)("XXX")5gbd+3e^3bd=(color(green)(bd))(5g+3e^3)#

Therefore:
#color(white)("XXX")25g^3v^3+15g^2e^3v^3+5gbd+3e^3bd#
#color(white)("XXXXXX")=(color(red)(5g^2v^3))(5g+3e^3)+(color(green)(bd))(5g+3e^3)#

Note 3:
#color(white)("XXX")#The second factor for each term is identical

#color(white)("XXX")25g^3v^3+15g^2e^3v^3+5gbd+3e^3bd#
#color(white)("XXXXXX")=(color(red)(5g^2v^3)+color(green)(bd))(5g+3e^3)#

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